{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 355,
   "id": "a1921d43",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import sympy as sp\n",
    "import sympy  as sp\n",
    "from sympy.matrices import Matrix\n",
    "from functools import partial\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits import mplot3d\n",
    "from math import pi\n",
    "import pprint\n",
    "pp=pprint.PrettyPrinter(indent=5)\n",
    "\n",
    "x,y,z,r,o=sp.symbols(\"x y z r theta\")\n",
    "#Tool Velocity Matrix\n",
    "\n",
    "\n",
    "X_BR=sp.Matrix([[400*sp.sin((2*np.pi*o)/50)*(2*np.pi)/5],[0],[400*sp.cos((2*np.pi*o)/50)*(2*np.pi)/5],[0],[0],[0]])\n",
    "X1_BR=sp.Matrix([[-320],[0],[0],[0],[0],[0]])\n",
    "X_FR=sp.Matrix([[-320],[0],[0],[0],[0],[0]])\n",
    "X1_FR=sp.Matrix([[320],[0],[0],[0],[0],[0]])\n",
    "X_BL=sp.Matrix([[-320],[0],[0],[0],[0],[0]])\n",
    "X1_BL=sp.Matrix([[-320],[0],[0],[0],[0],[0]])\n",
    "X_FL=sp.Matrix([[400*sp.sin((2*np.pi*o)/50)*(2*np.pi)/5],[0],[400*sp.cos((2*np.pi*o)/50)*(2*np.pi)/5],[0],[0],[0]])\n",
    "X1_FL=sp.Matrix([[-320],[0],[0],[0],[0],[0]])\n",
    "\n",
    "\n",
    "file_name='front_jump_gait.json'\n",
    "\n",
    "theta_i, alpha_i, d_i, a_i, A_i, a_3, d_1, d_3, d_5, d_7 = sp.symbols('theta_i alpha_i d_i a_i A_i a_3 d_1, d_3, d_5, d_7')\n",
    "theta_1,theta_2,theta_3,theta_4,theta_5,theta_6,theta_7 = sp.symbols ('theta_1,theta_2, theta_3, theta_4, theta_5, theta_6, theta_7')\n",
    "Rot_z = sp.Matrix([ [sp.cos(theta_i), -sp.sin(theta_i),0,0], [sp.sin(theta_i),sp.cos(theta_i),0,0], [0,0,1,0], [0,0,0,1] ]);\n",
    "Rot_x = sp.Matrix([ [1,0,0,0], [0,sp.cos(alpha_i), -sp.sin(alpha_i),0], [0, sp.sin(alpha_i), sp.cos(alpha_i), 0], [0,0,0,1] ]); \n",
    "Tran_z = sp.Matrix([[1,0,0,0], [0,1,0,0], [0,0,1,d_i], [0,0,0,1]])\n",
    "Tran_x = sp.Matrix([[1,0,0,a_i], [0,1,0,0], [0,0,1,0], [0,0,0,1]])\n",
    "\n",
    "A_i=Rot_z*Tran_z*Tran_x*Rot_x\n",
    "\n",
    "# Back Left Leg\n",
    "\n",
    "BL_Ad0=A_i.subs([(theta_i,math.radians(90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "BL_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BL_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,64.85)])\n",
    "BL_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,-140)])\n",
    "BL_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "BL_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BL_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "# Back Right Leg\n",
    "BR_Ad0=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "BR_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BR_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(-90)),(a_i,0),(d_i,64.85)])\n",
    "BR_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,140)])\n",
    "BR_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "BR_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BR_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "\n",
    "#Front Left Leg\n",
    "FL_Ad0=A_i.subs([(theta_i,math.radians(90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "FL_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FL_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,64.85)])\n",
    "FL_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,-140)])\n",
    "FL_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "FL_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FL_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "\n",
    "#Front Right Leg\n",
    "FR_Ad0=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "FR_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FR_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(-90)),(a_i,0),(d_i,-64.85)])\n",
    "FR_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,140)])\n",
    "FR_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "FR_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FR_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "\n",
    "T1=BR_Ad0*BR_A1\n",
    "T2=BR_Ad0*BR_A1*BR_Ad1*BR_A2\n",
    "T3=BR_Ad0*BR_A1*BR_Ad1*BR_A2*BR_Ad2*BR_A3\n",
    "T4=BR_Ad0*BR_A1*BR_Ad1*BR_A2*BR_Ad2*BR_A3*BR_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_BR = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "T1=BL_Ad0*BL_A1\n",
    "T2=BL_Ad0*BL_A1*BL_Ad1*BL_A2\n",
    "T3=BL_Ad0*BL_A1*BL_Ad1*BL_A2*BL_Ad2*BL_A3\n",
    "T4=BL_Ad0*BL_A1*BL_Ad1*BL_A2*BL_Ad2*BL_A3*BL_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_BL = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "T1=FL_Ad0*FL_A1\n",
    "T2=FL_Ad0*FL_A1*FL_Ad1*FL_A2\n",
    "T3=FL_Ad0*FL_A1*FL_Ad1*FL_A2*FL_Ad2*FL_A3\n",
    "T4=FL_Ad0*FL_A1*FL_Ad1*FL_A2*FL_Ad2*FL_A3*FL_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_FL = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "T1=FR_Ad0*FR_A1\n",
    "T2=FR_Ad0*FR_A1*FR_Ad1*FR_A2\n",
    "T3=FR_Ad0*FR_A1*FR_Ad1*FR_A2*FR_Ad2*FR_A3\n",
    "T4=FR_Ad0*FR_A1*FR_Ad1*FR_A2*FR_Ad2*FR_A3*FR_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_FR = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "id": "9a72d216",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "..................................................."
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "back_right_joint=[]\n",
    "T=T4\n",
    "x_tool_br=[]\n",
    "y_tool_br=[]\n",
    "z_tool_br=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=50:\n",
    "    if i<25:\n",
    "        X_eval=X_BR.subs(o,i)\n",
    "    if i>25:\n",
    "        X_eval=X1_BR.subs(o,j)\n",
    "        j+=1\n",
    "    back_right_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_br.append(T_eval[3])\n",
    "    y_tool_br.append(T_eval[7])\n",
    "    z_tool_br.append(T_eval[11])\n",
    "    J_eval=J_BR.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "id": "1e406526",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "..................................................."
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "front_right_joint=[]\n",
    "T=T4\n",
    "x_tool_fr=[]\n",
    "y_tool_fr=[]\n",
    "z_tool_fr=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=50:\n",
    "    if i<25:\n",
    "        X_eval=X_FR.subs(o,i)\n",
    "    if i>25:\n",
    "        X_eval=X1_FR.subs(o,j)\n",
    "        j+=1\n",
    "    front_right_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_fr.append(T_eval[3])\n",
    "    y_tool_fr.append(T_eval[7])\n",
    "    z_tool_fr.append(T_eval[11])\n",
    "    J_eval=J_FR.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "id": "3d70a9fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "..................................................."
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "front_left_joint=[]\n",
    "T=T4\n",
    "x_tool_fl=[]\n",
    "y_tool_fl=[]\n",
    "z_tool_fl=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=50:\n",
    "    if i<25:\n",
    "        X_eval=X_FL.subs(o,i)\n",
    "    if i>25:\n",
    "        X_eval=X1_FL.subs(o,j)\n",
    "        j+=1\n",
    "    front_left_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_fl.append(T_eval[3])\n",
    "    y_tool_fl.append(T_eval[7])\n",
    "    z_tool_fl.append(T_eval[11])\n",
    "    J_eval=J_FL.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "id": "8f30a51c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "..................................................."
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "back_left_joint=[]\n",
    "T=T4\n",
    "x_tool_bl=[]\n",
    "y_tool_bl=[]\n",
    "z_tool_bl=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=50:\n",
    "    if i<25:\n",
    "        X_eval=X_BL.subs(o,i)\n",
    "    if i>25:\n",
    "        X_eval=X1_BL.subs(o,j)\n",
    "        j+=1\n",
    "    back_left_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_bl.append(T_eval[3])\n",
    "    y_tool_bl.append(T_eval[7])\n",
    "    z_tool_bl.append(T_eval[11])\n",
    "    J_eval=J_BL.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "id": "aebbe8d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create a grid of subplots with 2 rows and 2 columns\n",
    "fig, axs = plt.subplots(2, 2)\n",
    "\n",
    "# Plot 1: Top left subplot\n",
    "axs[0, 0].plot(x_tool_br, z_tool_br)\n",
    "axs[0, 0].set_xlabel(\"y coordinate\")\n",
    "axs[0, 0].set_ylabel(\"z coordinate\")\n",
    "axs[0, 0].set_title(\"Trajectory of Back Right Leg\")\n",
    "axs[0, 0].axis(\"equal\")\n",
    "axs[0, 0].grid(True)\n",
    "\n",
    "# Plot 2: Top right subplot\n",
    "axs[0, 1].plot(x_tool_bl, z_tool_bl)  # Replace with your desired plot\n",
    "axs[0, 1].set_xlabel(\"y\")\n",
    "axs[0, 1].set_ylabel(\"z\")\n",
    "axs[0, 1].set_title(\"Trajectory of Back Left Leg\")\n",
    "axs[0, 1].axis(\"equal\")\n",
    "axs[0, 1].grid(True)\n",
    "# Add other formatting and plotting commands as needed\n",
    "\n",
    "# Plot 3: Bottom left subplot\n",
    "axs[1, 0].plot(x_tool_fr, z_tool_fr)  # Replace with your desired plot\n",
    "axs[1, 0].set_xlabel(\"y\")\n",
    "axs[1, 0].set_ylabel(\"z\")\n",
    "axs[1, 0].set_title(\"Trajectory of Front Right Leg\")\n",
    "axs[1, 0].axis(\"equal\")\n",
    "axs[1, 0].grid(True)\n",
    "# Add other formatting and plotting commands as needed\n",
    "\n",
    "# Plot 4: Bottom right subplot\n",
    "axs[1, 1].plot(x_tool_fl, z_tool_fl)  # Replace with your desired plot\n",
    "axs[1, 1].set_xlabel(\"y\")\n",
    "axs[1, 1].set_ylabel(\"z\")\n",
    "axs[1, 1].set_title(\"Trajectory of Front Left Leg\")\n",
    "axs[1,1].axis(\"equal\")\n",
    "axs[1,1].grid(True)\n",
    "# Add other formatting and plotting commands as needed\n",
    "\n",
    "# Adjust the layout to avoid overlapping titles and labels\n",
    "fig.tight_layout()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "id": "4d3aa0e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0, -0.7, 1.5],\n",
       " [2.10920844107693e-8, -0.735108227846018, 1.57793213143621],\n",
       " [4.53998094029623e-8, -0.763586679628283, 1.65220706403443],\n",
       " [7.35942694646058e-8, -0.784649426149904, 1.72211285698553],\n",
       " [1.06401461329381e-7, -0.797541254452395, 1.78687074865323],\n",
       " [1.44551375619526e-7, -0.801592941255934, 1.84563413977346],\n",
       " [1.88675771605676e-7, -0.796297919132879, 1.89749824393029],\n",
       " [2.39131619728067e-7, -0.781407479771501, 1.94152436382964],\n",
       " [2.95737055766451e-7, -0.757033481254323, 1.97678246506597],\n",
       " [3.57441518638802e-7, -0.723736740542878, 2.00241344514774],\n",
       " [4.22017281947999e-7, -0.682570113912189, 2.01770749463274],\n",
       " [4.85933687466772e-7, -0.635045303044944, 2.02218764023385],\n",
       " [5.44594817692500e-7, -0.583008770325821, 2.01568057161337],\n",
       " [5.93015951095628e-7, -0.528443549055993, 1.99835476043003],\n",
       " [6.26794013266551e-7, -0.473245642288958, 1.97071240767690],\n",
       " [6.43029873172478e-7, -0.419035652672836, 1.93353575963948],\n",
       " [6.40850230574224e-7, -0.367049257294852, 1.88780293302059],\n",
       " [6.21374509466215e-7, -0.318115838211532, 1.83459572654848],\n",
       " [5.87227763084501e-7, -0.272704702581637, 1.77501932274292],\n",
       " [5.41847845905676e-7, -0.231006234187108, 1.71014501695209],\n",
       " [4.88827951066117e-7, -0.193019532563643, 1.64097800807148],\n",
       " [4.31437100199464e-7, -0.158629455317959, 1.56844649711683],\n",
       " [3.72354544697054e-7, -0.127666654308487, 1.49340633446660],\n",
       " [3.13584980121745e-7, -0.0999509900414753, 1.41665595688765],\n",
       " [2.56495332858109e-7, -0.0753217893266647, 1.33895790414614],\n",
       " [2.01916476232701e-7, -0.0536591301870256, 1.26106485635198],\n",
       " [1.50971521780885e-7, -0.0288651212175886, 1.17857056462044],\n",
       " [1.50172094744163e-7, -0.0604697561036246, 1.20906470224319],\n",
       " [1.48539210107198e-7, -0.0916795393141143, 1.23797709789466],\n",
       " [1.46120789423865e-7, -0.122532446293057, 1.26538587460915],\n",
       " [1.42958315664003e-7, -0.153059414632736, 1.29135618664461],\n",
       " [1.39088482555528e-7, -0.183285355723950, 1.31594250861890],\n",
       " [1.34544470836113e-7, -0.213229935439264, 1.33919043633225],\n",
       " [1.29356949519091e-7, -0.242908184467190, 1.36113812485294],\n",
       " [1.23554869274018e-7, -0.272330981817918, 1.38181745310651],\n",
       " [1.17166094449307e-7, -0.301505443396225, 1.40125497944072],\n",
       " [1.10217906282558e-7, -0.330435239471513, 1.41947273541618],\n",
       " [1.02737400300114e-7, -0.359120859167904, 1.43648889287368],\n",
       " [9.47517942677761e-8, -0.387559835977281, 1.45231833054255],\n",
       " [8.62886585018011e-8, -0.415746945258929, 1.46697312002343],\n",
       " [7.73760772111919e-8, -0.443674382392200, 1.48046294620376],\n",
       " [6.80427474649752e-8, -0.471331928463527, 1.49279547357077],\n",
       " [5.83180210914106e-8, -0.498707108937962, 1.50397666715026],\n",
       " [4.82318940970447e-8, -0.525785349579092, 1.51401107469372],\n",
       " [3.78149478990506e-8, -0.552550132864479, 1.52290207510426],\n",
       " [2.70982467167673e-8, -0.578983157246079, 1.53065209681931],\n",
       " [1.61131957125198e-8, -0.605064500793261, 1.53726280887587],\n",
       " [4.89136482784745e-9, -0.630772790010796, 1.54273528661130],\n",
       " [-6.53571623739176e-9, -0.656085373935635, 1.54707015335744],\n",
       " [-1.81367861077651e-8, -0.680978502982508, 1.55026769903245],\n",
       " [-2.98810966821587e-8, -0.705427511432203, 1.55232797619866]]"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "front_left_joint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "id": "cffe940f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0, -0.7, 1.5],\n",
       " [-1.13099434435882e-8, -0.723013052356928, 1.50005012852982],\n",
       " [-2.27036025569893e-8, -0.745506767868113, 1.49895974526541],\n",
       " [-3.41578458478223e-8, -0.767456547736724, 1.49672837456132],\n",
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       " [-5.71634892893025e-8, -0.809625275978752, 1.48883927765579],\n",
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